3. (10 Points) You are given the following multiple-decrement table where (x) is at the beginning of the year: d}(2) 2,000 60 ) (3) 1,000 900 61 1,900 62 IX 100,000 93,000 86,300 79,900 73,800 68,000 dx (1) 4,000 3,900 3,800 3,700 3,600 3,500 800 700 63 1,800 1,700 1,600 1,500 64 600 500 65 Now assuming the following for the dependent rates of decrement: i. decrement 1 is uniformly distributed between integer ages ii. 1/3 of decrement 2 occurs at the beginning of the year and 2/3 occurs at the end of the year iii. decrement 3 occurs exactly 6 months into the year a) (2 points): Determine the probability that (61) survives 2 years, then transitions to state (2) or state (3) within the following two years (i.e. transitions in year 3 or 4) () b) (2 points) Calculate 0.6p.2 (also denoted byo.6p) 1) 2) 3) c) (6 points) Calculate 962", 962', and 962 (the independent rates of decrement, also denoted by 962", 962, *(2) and 3. (10 Points) You are given the following multiple-decrement table where (x) is at the beginning of the year: d}(2) 2,000 60 ) (3) 1,000 900 61 1,900 62 IX 100,000 93,000 86,300 79,900 73,800 68,000 dx (1) 4,000 3,900 3,800 3,700 3,600 3,500 800 700 63 1,800 1,700 1,600 1,500 64 600 500 65 Now assuming the following for the dependent rates of decrement: i. decrement 1 is uniformly distributed between integer ages ii. 1/3 of decrement 2 occurs at the beginning of the year and 2/3 occurs at the end of the year iii. decrement 3 occurs exactly 6 months into the year a) (2 points): Determine the probability that (61) survives 2 years, then transitions to state (2) or state (3) within the following two years (i.e. transitions in year 3 or 4) () b) (2 points) Calculate 0.6p.2 (also denoted byo.6p) 1) 2) 3) c) (6 points) Calculate 962", 962', and 962 (the independent rates of decrement, also denoted by 962", 962, *(2) and